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On the Mixed Dirichlet–Steklov-Type and Steklov-Type Biharmonic Problems in Weighted Spaces

1
Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Vavilov str., 40, Moscow 119333, Russia
2
Moscow Aviation Institute (National Research University), Volokolomskoe Shosse, 4, Moscow 125993, Russia
Math. Comput. Appl. 2019, 24(1), 25; https://doi.org/10.3390/mca24010025
Received: 31 January 2019 / Revised: 15 February 2019 / Accepted: 16 February 2019 / Published: 18 February 2019
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
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Abstract

We studied the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we studied the unique solvability of the mixed Dirichlet–Steklov-type and Steklov-type biharmonic problems in the exterior of a compact set under the assumption that generalized solutions of these problems has a bounded Dirichlet integral with weight | x | a. Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of these problems or present exact formulas for the dimension of the space of solutions. View Full-Text
Keywords: biharmonic operator; mixed Dirichlet–Steklov-type problem; Steklov-type problem; Dirichlet integral; weighted spaces biharmonic operator; mixed Dirichlet–Steklov-type problem; Steklov-type problem; Dirichlet integral; weighted spaces
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Matevossian, H. On the Mixed Dirichlet–Steklov-Type and Steklov-Type Biharmonic Problems in Weighted Spaces. Math. Comput. Appl. 2019, 24, 25.

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